Tennant had been the original choice to lead the show back on to the screens in March 2005 but the role was given to Christopher Ecclestone.

Tennant took over from him after just one series.

Since he took over the controls of the famous time machine viewing figures have gone through the roof - with the show regularly attracting as many eight million fans.

The BBC has refused to confirm or deny the news.

A spokesman said: "We have been told not to say anything about this."

Viewers on internet fan sites were quick to react to the news.

Sebastian J Brook, who runs the Doctor Who Online fan club, said: "If the news of Tennant leaving is indeed true, it will hit fans hard.

"He has proved to be one of the best-loved actors to play the role of the doctor. Our forum membership are always singing his praises."

He added: "It's going to be hard to find someone with Tennant's energy, enthusiasm, sheer talent and drive."

But industry insiders suggested that the move might accompany a change in the production team.

A source told the Sunday Express: "We believe that Russell T Davies, the executive producer, will be leaving after the next series with Phil Collinson, the producer, who is moving across to Coronation Street.

"I am sure David chose to leave, but it was probably because everything's changing.

"One of the ways of keeping Doctor Who fresh, and fans consistently interested, is by reinventing the main characters often."

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Quitting: Catherine Tate has hinted that her fellow Doctor Who star could be quitting the show

James Nesbitt is the 3/1 favourite to replace David Tennant as Doctor Who, according to Ladbrokes.

And Welshman Rhys Ifans is 5/1 to land the role.

Ladbrokes spokesman, Nick Weinberg, said: "If David Tennant quits there will be no shortage of people interested in taking over. Doctor Who is a British institution.